The expansion of the universe is its accelerating growth, driven by dark energy.The universe expands like raisin dough in the oven: each raisin galaxy moves away from the others, and the farther away, the faster. The dough itself is space, which is getting bigger.
Theoretical foundations emerged in 1917 when Einstein added the cosmological constant for a static universe. In 1922–1924, Alexander Friedmann found non-stationary solutions to Einstein's equations, predicting expansion. In 1927, Georges Lemaître independently obtained the same solutions and compared them with Slipher's redshift data, proposing the concept of a 'primeval atom.' Edwin Hubble in 1929, based on observations by Vesto Slipher and Milton Humason, confirmed the linear relationship between redshift and distance. In 1964, Arno Penzias and Robert Wilson accidentally discovered the cosmic microwave background, which became decisive evidence for a hot beginning and expansion.
The expansion is described by the FLRW metric: ds^2 = -c^2 dt^2 + a(t)^2 [dr^2/(1 - k r^2) + r^2 (dθ^2 + sin^2θ dφ^2)], where a(t) is the scale factor, k is the curvature parameter (-1, 0, +1). The evolution of a(t) is given by the Friedmann equations: (ȧ/a)^2 = (8πGρ + Λc^2)/3 - kc^2/a^2, and ä/a = -(4πG/3)(ρ + 3p/c^2) + Λc^2/3. In the current era, dark energy (Λ>0) dominates, leading to accelerated expansion. Redshift z is defined as 1+z = a(t_obs)/a(t_em). The Hubble law in the first approximation: v = H₀ D, where the Hubble constant H₀ ≈ 70 (km/s)/Mpc.
Light from the most distant galaxies has traveled to us for billions of years, and during that time, space has stretched so much that the light has become invisible to the eye—turning into microwave radiation.
| H | variable | Hubble parameter — hubble parameter per second |
| z | variable | redshift — redshift |
| H0 | variable | Hubble constant — hubble constant per second |
| Ωm | variable | matter density parameter — density parameter |
| Ωr | variable | radiation density parameter — density parameter |
| Ωk | variable | curvature density parameter — density parameter |
| ΩΛ | variable | cosmological constant density parameter — density parameter |
| Ωx | variable | dark energy density parameter (general) — density parameter |
| f(z) | variable | dark energy equation-of-state function — equation of state function |
| sqrt | operator | square root — square root |













